chapt9 - Los Angeles polution mortality study Shumway at al...

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Unformatted text preview: Los Angeles polution mortality study Shumway at al (1988) Environ. Res. 45, 224-241 Los Angeles County: average daily cardiovascular mortality particulate polution (six day smoothed averages) n = 508, 1970-1979 Bivariate time series Correlation is largest at 8 weeks lag, but ... acf ccf Stat 153 - 29 Oct 2008 D. R. Brillinger Chapter 9 - Linear Systems [ 1 x 1 + 2 x 2 ](t) = 1 [x 1 ](t) + 2 [x 2 ](t) Time invariant . [B x](t) = B [x](t) [B x](t) = y(t- ) if [x](t) = y(t) Linear. Example. How to describe ? =- =- k k h k t t x y Common in nature System identification Y t = h k X t-k + N t Is there a relationship? Estimate h, H given {x(t),y(t)}, t=0,...,N Predict Y from X Control Studying causality Studying delay =- =- k k h k t t x y { h k }: impulse response Define k = 1 if k = 0 and = otherwise, then =- =- k k t k t h h h k = 0 k<0: causal/physically realizable One way Transfer / frequency response function - = k k i k e h H ) ( G( ) = |H()|: gain () = arg{H()} : phase complex-valued H(+2) = H() H(-) = H() * complex conjugate Another way Example....
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This note was uploaded on 10/19/2009 for the course MATH 611 taught by Professor Jsdkasj during the Spring '09 term at Kansas.

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chapt9 - Los Angeles polution mortality study Shumway at al...

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